# Python __rmatmul__() Magic Method

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## Syntax

`object.__rmatmul__(self, other)`

The Python `__rmatmul__()` method implements the reverse matrix multiplication `@` operation with reflected, swapped operands. So, when you call `x @ y`, Python attempts to call `x.__matmul__(y)`. If the method is not implemented, Python attempts to call `__rmatmul__` on the right operand and if this isn’t implemented either, it raises a `TypeError`.

We call this a “Dunder Method” for Double Underscore Method” (also called “magic method”). To get a list of all dunder methods with explanation, check out our dunder cheat sheet article on this blog.

## Background Matrix Multiplication

In the following example, you create a custom class `Data` and overwrite the `__matmul__()` method that simply returns a dummy string. The real computation could be much more sophisticated, of course.

```class Data:

def __matmul__(self, other):
return '... my result of matmul...'

a = Data()
b = Data()
c = a @ b

print(c)
# ... my result of matmul...```

The `@` operator was introduced to Python’s core syntax from 3.5 onwards thanks to PEP 465. Its only goal is to solve the problem of matrix multiplication. It even comes with a nice mnemonic – `@` is * for mATrices.

It is unusual that `@` was added to the core Python language when it’s only used with certain libraries. Fortunately, the only other time we use `@` is for decorator functions. So you are unlikely to get confused.

## Python __matmul__ vs __rmatmul__

Say, you want to calculate the `@` operation on two custom objects `x` and `y`:

`print(x @ y)`

Python first tries to call the left object’s `__matmul__()` method `x.__matmul__(y)`. But this may fail for two reasons:

1. The method `x.__matmul__()` is not implemented in the first place, or
2. The method `x.__matmul__()` is implemented but returns a `NotImplemented` value indicating that the data types are incompatible.

If this fails, Python tries to fix it by calling the `y.__rmatmul__()` for reverse matrix multiplication on the right operand `y`.

If the reverse matrix multiplication method is implemented, Python knows that it doesn’t run into a potential problem of a non-commutative operation. If it would just execute `y.__matmul__(x)` instead of `x.__matmul__(y)`, the result would be wrong because the operation may be non-commutative when defined as a custom operation. That’s why `y.__rmatmul__(x)` is needed.

So, the difference between `x.__matmul__(y)` and `x.__rmatmul__(y)` is that the former calculates `x @ y` whereas the latter calculates `y @ x` — both calling the respective method defined on the object `x`.

A nice little trick is to indirectly define matrix multiplication on a data type that doesn’t support it and that cannot be altered — such as a basic data type like a list — by implementing` __rmatmul__` on the other custom class over which one may have control.

You can see this in effect here where we attempt to call the operation on the left operand `x`—but as it’s not implemented, Python simply calls the reverse operation on the right operand `y`.

```class Data_1:
pass

class Data_2:
def __rmatmul__(self, other):
return 'called reverse matmul'

x = Data_1()
y = Data_2()

print(x @ y)
# called reverse matmul
```

## Related Video

To understand this operation in detail, feel free to read over our tutorial or watch the following video:

References:

## Where to Go From Here?

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